Question

Guys help me.
it has troubled me alot.​

Answer 1

Answer:

I thought that answer is:

1.√11

Answer 2

Step-by-step explanation:

$\sqrt{17 + x \sqrt{11} } = \sqrt{11} + \sqrt{6} \\ sqaring \: \: both \: \: \: sides \\ we \: \: get \\ ( \sqrt{(17 + x \sqrt{11} })) {}^{2} = (\sqrt{11} + \sqrt{6}) {}^{2} \\ \\ 17 + x \sqrt{11} = (\sqrt{11}) {}^{2} + 2 \times \sqrt{11} . \sqrt{6} + (\sqrt{6} ) {}^{2} \\ \\ 17 + x \sqrt{11} = 11 + 2 \sqrt{6} . \sqrt{11} + 6 \\ \\ 17 + x \sqrt{11} = 17 + 2 \sqrt{6} . \sqrt{11} \\ \\ x \sqrt{11} = 2 \sqrt{6} . \sqrt{11} \\ \\ x = 2 \sqrt{6}$

Now

${x}^{2} =(2\sqrt{6} ) {}^{2}\\ \\ =4×6\\\\=24$

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